Your house is dirty. You want to clean your house. You start by cleaning your bedroom, even though other rooms are also dirty. You might clean them later. You might never manage to clean out your storage closet. Are you a virtue-signalling hypocrite for saying you want to clean your house? Or is there some nuance?
Put it another way. I believe in trying to lower my environmental footprint. I recycle. I compost sometimes (not great, though, my building doesn't have a great setup for it). I grow some of my own food. I try to buy local stuff when I can and I am lucky enough to live in a place where a lot of food is produced locally. I drive a hybrid and take the bus. I try to buy high-efficiency devices like LED lights. I try to turn off the TV when I'm not in the room. I buy carbon offsets when I fly. I vote for politicians who support environmental policies. I support environmental charities.
But I also eat meat, and order some things online from Amazon, and don't always eat local and still keep my car and didn't buy an electric car and I don't recycle my shower water to water my garden like some people do and I have the air conditioning on right now. And I like to watch TV and movies, and I probably have my TV on more of the day than I should, and I could bicycle to work instead of bus, and...
Am I a virtue-signalling hypocrite? You can say yes, I promise I have no intention of banning anyone who argues with me, I'm not trying to lure you into a trap even though you just admitted you were trying to lure the people you disagree with into a trap. Because I would say that I do what I can, I try to make little good decisions when I can, especially ones that I can implement at no cost to me, but I'm not perfect, I will never be perfect, but I try to do better, I try to think about what I do rather than just be mindless. It's easier for me to pick an LED bulb up off the shelf next to an incandescent. It would be difficult for me, as someone making my living doing research and programming, to shut off all my electronics. My city isn't really bike safe and I like to sleep in a bit so I don't really have time to bike to work and then clean up before my day starts. If you think I don't really believe what I say I do, then call me out. I'm a living example of what you're getting at. Please call me a hypocrite, I yearn to be shamed.
Okay, now to get to your actual point, about the nature of ethical boycotts. First, I think one of the considerations someone weighs when considering an ethical boycott is the level of connection between the product and the outcome they don't like. For example, let's say you are pro-life and you do not want to support products that are associated with abortion. Maybe you wouldn't go buy the Planned Parenthood Abortion Chocolate Bar, Dedicated To Abortion Forever. But maybe you'd still be willing to buy, like, a car if the car company did some tiny charity work with a women's group that supports abortion (or maybe you wouldn't be! It's ok! It's your decision!) Maybe you wouldn't see a film where the director donates a lot of money to Planned Parenthood and speaks out on abortion. But maybe you would see a film where the assistant cameraman and his wife had an abortion. As an adult, you are probably capable of understanding that nuance exists.
Your example was that non-Americans should boycott all American video games because the US government does bad things with its military. Setting aside that this is a crazy level of indirection, so it's obviously a very bad example and a very stupid argument (that you made because, as you admit, you weren't interested in making a point, just pantsing dumb liberals), how exactly does this expose liberals as hypocrites? I think if someone doesn't want to be involved with US goods because they feel it's an ethical breach to be complicit in the US government, more power to them. I don't make that choice for me and I don't think it's practical, but if someone wants to make that choice for them, like, okay?
Also related to the topic, I think if someone finds military porn and bombing the shit out of other countries distasteful, actually it is worth considering whether or not they want to support entertainment products that support those practices. I don't play a lot of military shooters because I'm not very interested in them, and one of the main reasons that I'm not very interested in them because of their content. I'm not for "censorship", but I also don't plan to buy them. Wow, liberals owned if they don't like Call of Duty? Or if they do? I can't really follow the argument.